Geodesic
Creation of solitons for sine-Gordon and Korteweg–de Vries equations by means of connections defining the representations of zero curvature
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 72-80

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It is possible to create traveling wave type solutions (and in particular soliton solutions) of partial differential equations by means of connections defining the representations of zero curvature. In this paper we create the solitons of the sine-Gordon equation and the Korteweg–de Vries equation. In the final section we compare the proposed method for soliton creation with the inverse scattering method. We systematically use the Cartan–Laptev invariant analytic method in the work.
Keywords: connection in principal bundle, connection in associated bundle, connection defining the representation of zero curvature, differential equation, Bäcklund maps.
Mots-clés : solitons 
@article{UZKU_2011_153_3_a6,
     author = {A. K. Rybnikov},
     title = {Creation of solitons for {sine-Gordon} and {Korteweg{\textendash}de~Vries} equations by means of connections defining the representations of zero curvature},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {72--80},
     publisher = {mathdoc},
     volume = {153},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a6/}
}
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A. K. Rybnikov. Creation of solitons for sine-Gordon and Korteweg–de Vries equations by means of connections defining the representations of zero curvature. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 72-80. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a6/